Financial markets with volatility uncertainty

Vorbrink J (2014)
Journal of Mathematical Economics 53: 64-78.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Vorbrink, Jörg
Abstract / Bemerkung
We investigate financial markets under model risk caused by uncertain volatilities. To this end, we consider a financial market that features volatility uncertainty. We use the notion of G-expectation and its corresponding G-Brownian motion recently introduced by Peng (2007) to ensure a mathematically consistent framework. Our financial market consists of a riskless asset and a risky stock with price process modeled by geometric G-Brownian motion. We adapt the notion of arbitrage to this more complex situation, and consider stock price dynamics which exclude arbitrage opportunities. Volatility uncertainty results in an incomplete market. We establish the interval of no-arbitrage prices for general European contingent claims, and deduce explicit results in the Markovian case.
Stichworte
incomplete markets; Volatility uncertainty; G-Brownian motion stochastic calculus; Pricing of contingent claims
Erscheinungsjahr
2014
Zeitschriftentitel
Journal of Mathematical Economics
Band
53
Seite(n)
64-78
ISSN
0304-4068
Page URI
https://pub.uni-bielefeld.de/record/2689692

Zitieren

Vorbrink J. Financial markets with volatility uncertainty. Journal of Mathematical Economics. 2014;53:64-78.
Vorbrink, J. (2014). Financial markets with volatility uncertainty. Journal of Mathematical Economics, 53, 64-78. doi:10.1016/j.jmateco.2014.05.008
Vorbrink, J. (2014). Financial markets with volatility uncertainty. Journal of Mathematical Economics 53, 64-78.
Vorbrink, J., 2014. Financial markets with volatility uncertainty. Journal of Mathematical Economics, 53, p 64-78.
J. Vorbrink, “Financial markets with volatility uncertainty”, Journal of Mathematical Economics, vol. 53, 2014, pp. 64-78.
Vorbrink, J.: Financial markets with volatility uncertainty. Journal of Mathematical Economics. 53, 64-78 (2014).
Vorbrink, Jörg. “Financial markets with volatility uncertainty”. Journal of Mathematical Economics 53 (2014): 64-78.

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